- Calculus, Volume 1: One Variable Calculus, with an Introduction to Linear Algebra
- Tom M. Apostol
- Second Edition
- 1967
- 978-1-119-49673-1
13.25. Miscellaneous review exercises on conic sections
- The line $x - y + 4 = 0$ is tangent to the parabola $y^2 = 16x.$ Find the point of contact.
- Find $(x, y)$ such that $x - y + 4= 0$ and $y^2 = 16x$
- $$\displaylines{y = x + 4; \quad y^2 = 16\\ \rightarrow x^2 + 8x + 16 = 16x\\ \rightarrow (x - 4)^2 = 0\\ \rightarrow x = 4,\quad y = 8 \quad \blacksquare}$$